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Simplifying -16t2 + 96t + 400 = 0 Reorder the terms: 400 + 96t + -16t2 = 0 Solving 400 + 96t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(25 + 6t + -1t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(25 + 6t + -1t2)' equal to zero and attempt to solve: Simplifying 25 + 6t + -1t2 = 0 Solving 25 + 6t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -25 + -6t + t2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + -6t + 25 + t2 = 0 + 25 Reorder the terms: -25 + 25 + -6t + t2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -6t + t2 = 0 + 25 -6t + t2 = 0 + 25 Combine like terms: 0 + 25 = 25 -6t + t2 = 25 The t term is -6t. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6t + 9 + t2 = 25 + 9 Reorder the terms: 9 + -6t + t2 = 25 + 9 Combine like terms: 25 + 9 = 34 9 + -6t + t2 = 34 Factor a perfect square on the left side: (t + -3)(t + -3) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (t + -3) equal to 5.830951895 and -5.830951895.Subproblem 1
t + -3 = 5.830951895 Simplifying t + -3 = 5.830951895 Reorder the terms: -3 + t = 5.830951895 Solving -3 + t = 5.830951895 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 5.830951895 + 3 Combine like terms: -3 + 3 = 0 0 + t = 5.830951895 + 3 t = 5.830951895 + 3 Combine like terms: 5.830951895 + 3 = 8.830951895 t = 8.830951895 Simplifying t = 8.830951895Subproblem 2
t + -3 = -5.830951895 Simplifying t + -3 = -5.830951895 Reorder the terms: -3 + t = -5.830951895 Solving -3 + t = -5.830951895 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = -5.830951895 + 3 Combine like terms: -3 + 3 = 0 0 + t = -5.830951895 + 3 t = -5.830951895 + 3 Combine like terms: -5.830951895 + 3 = -2.830951895 t = -2.830951895 Simplifying t = -2.830951895Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.830951895, -2.830951895}Solution
t = {8.830951895, -2.830951895}
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